A HIGH-RESOLUTION FINITE-DIFFERENCE SCHEME FOR NONUNIFORM GRIDS

A higher-order, high-resolution finite-difference scheme for nonunifor m grids is presented. This scheme, derived rigorously form Taylor seri es expansion at nomuniform gridpoints with a total-variation-diminishi ng constraint applied, gives better numerical approximations to the an alytical solutions compared with schemes that are only first-order whe n applied to nonuniform grids. The scheme is suitable even for extreme ly nonuniform grids, which are often required in large-scale simulatio n problems. A wide range of flexibility in designing nonuniform grids is achieved.